A movie theater offers a special pricing for membership. The normal cost is $8\$8$8 per ticket. The membership costs $5.50\$5.50$5.50 per ticket but an initial fee of $60\$60$60 . After how many tickets are both options the same price?

Answer 1

To find out after how many tickets the total cost of both options becomes the same, we can set up an equation.

Let \( n \) represent the number of tickets purchased.

1. The total cost for a non-member (normal pricing) for \( n \) tickets is given by: \[ \text{Cost}_{\text{normal}} = 8n \]

2. The total cost for a member is the sum of the initial membership fee and the cost of tickets at the member rate: \[ \text{Cost}_{\text{member}} = 60 + 5.5n \]

We need to find the value of \( n \) where the two costs are equal: \[ 8n = 60 + 5.5n \]

Now we can solve this equation for \( n \):

1. Subtract \( 5.5n \) from both sides: \[ 8n - 5.5n = 60 \] \[ 2.5n = 60 \]

2. Now divide both sides by \( 2.5 \): \[ n = \frac{60}{2.5} = 24 \]

Thus, after purchasing 24 tickets, both pricing options will cost the same. The answer is: \[ \boxed{24} \]